A325979 Odd numbers k for which gcd(A325977(k), A325978(k)) is equal to abs(A325978(k)).

1, 3465, 72981, 78651, 80937, 152703, 199341, 201771, 241605, 253287, 492507, 631881, 880821, 933147, 985473, 1063755, 1209285, 1244133, 1292445, 1313235, 1327095, 1347885, 1360881, 1451835, 1521135, 1597365, 1620375, 1814373, 2015475, 2664585, 6058233, 6676371, 8186751, 11119761, 17496243, 18379935, 28695627

Offset

1,2

Comments

Provided that A325977(k) and A325978(k) are never zero for the same k, these are odd numbers k such that A325978(k) is not zero and divides A325977(k).

Of the first 65 terms, only a(5) = 80937 and a(51) = 86086881 are in A228058.

Links

Giovanni Resta, Table of n, a(n) for n = 1..281 (terms < 10^12; first 65 terms from Antti Karttunen)

Index entries for sequences where any odd perfect numbers must occur.

Prog

(PARI)
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A034460(n) = (A034448(n) - n);
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A325313(n) = (A048250(n) - n);
A325977(n) = ((A034460(n)+A325313(n))/2);
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325314(n) = (n - A162296(n));
A048146(n) = (sigma(n)-A034448(n));
A325814(n) = (n-A048146(n));
A325978(n) = ((A325314(n)+A325814(n))/2);
A325975(n) = gcd(A325977(n), A325978(n));
isA325979(n) = ((n%2)&&(A325975(n)==abs(A325978(n))));
\\ Or alternatively as:
isA325979(n) = if(!(n%2), 0, my(x = A325977(n), y = A325978(n)); (!x&&!y)||(y&&!(x%y)));

Crossrefs

Cf. A228058, A325975, A325977, A325978, A325981.

Sequence in context: A307098 A251531 A251526 * A251525 A176268 A031357

Adjacent sequences: A325976 A325977 A325978 * A325980 A325981 A325982

Keyword

nonn

Author

Antti Karttunen, Jun 02 2019

Status

approved